Week 4 January 25th

Week 4 January 25th

The Physics of Music

“Everything is determined … by forces over which we have no control. It is determined for the insects as well as for the star. Human beings, vegetables, or cosmic dust – we all dance to a mysterious tune, intoned in the distance by an invisible piper.”

– Albert Einstein

Objectives:
1. Students will make a double bubble map on the differences and similarities of water waves and sound waves.

2. Students will take a quiz on graphing sine waves and finding the equations.

3. Students will

Agenda:
1. Music ppt slides 42-60 damping functions
2. Tacoma bridge / Natural Frequency / Mythbusters video on collapsing bridge.
3. Sound canceling slides from Music ppt. slides #13-19
4. Sound and Music WS (on thumbdrive)
5. Graphing Sine Waves WS & Quiz
6. Physics and Music Ppt. - Guest Speaker on the physics of music.
7. Cornell notes on different music terms presented in Physics and Music Ppt.

Helpful Websites:
http://cnx.org/content/m12373/latest/
http://cnx.org/content/m11060/latest/
http://www.sciencejoywagon.com/physicszone/09waves/
http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroSound.xml

http://phet.colorado.edu/simulations/sims.php?sim=Microwaves

Notes:
Resonance:

In physics, resonance is the tendency of a system to oscillate at larger amplitude at some frequencies than at others. These are known as the system's resonance frequencies (or resonant frequencies). At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system stores vibrational energy. When damping is small, the resonance frequency is approximately equal to the natural frequency of the system, which is the frequency of free vibrations. Resonant phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, Nuclear Magnetic Resonance (NMR), Electron Spin Resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies.

One familiar example is a playground swing, which acts as a pendulum. Pushing a person in a swing in time with the natural interval of the swing (its resonance frequency) will make the swing go higher and higher (maximum amplitude), while attempts to push the swing at a faster or slower tempo will result in smaller arcs. This is because the energy the swing absorbs is maximized when the pushes are 'in phase' with the swing's oscillations, while some of the swing's energy is actually extracted by the opposing force of the pushes when they are not.
Resonance occurs widely in nature, and is exploited in many man-made devices. It is the mechanism by which virtually all sinusoidal waves and vibrations are generated. Many sounds we hear, such as when hard objects of metal, glass, or wood are struck, are caused by brief resonant vibrations in the object.

Damping:

Damping is any effect, either deliberately engendered or inherent to a system, that tends to reduce the amplitude of oscillations of an oscillatory system.
In real oscillators friction, or damping, slows the motion of the system. In many vibrating systems the frictional force Ff can be modeled as being proportional to the velocity v of the object: Ff = −cv, where c is the viscous damping coefficient, given in units of newton-seconds per meter.

Similar damped oscillator behavior occurs for a diverse range of disciplines that include control engineering, mechanical engineering and electrical engineering. The physical quantity that is oscillating varies greatly, and could be the swaying of a tall building in the wind, the speed of an electric motor, or the current through a RLC circuit.

The value of the damping ratio ς critically determines the behavior of the damped system. In particular a damped harmonic oscillator can be:

Overdamped (ς > 1): The system returns (exponentially decays) to equilibrium without oscillating. Larger values of the damping ratio ς return to equilibrium slower.

Critically damped (ς = 1): The system returns to equilibrium as quickly as possible without oscillating. This is often desired for the damping of systems such as doors.

Underdamped (ς <>


http://mathdemos.gcsu.edu/mathdemos/trigsounddemo/trigsounddemo.html